R: Finding Mardia's multivariate skewness

mardiaSkew {semTools} | R Documentation

## Finding Mardia's multivariate skewness

### Description

Finding Mardia's multivariate skewness of multiple variables

### Usage

    mardiaSkew(dat, use = "everything")

### Arguments

`dat` | The target matrix or data frame with multiple variables
`use` | Missing data handling method from the `cov` function.

### Details

The Mardia's multivariate skewness formula (Mardia, 1970) is

b_{1, d} = \frac{1}{n^2}∑^n_{i=1}∑^n_{j=1}≤ft[ ≤ft(\bold{X}_i - \bold{\bar{X}} \right)^{'} \bold{S}^{-1} ≤ft(\bold{X}_j - \bold{\bar{X}} \right) \right]^3,

where d is the number of variables, X is the target dataset with multiple variables, n is the sample size, \bold{S} is the sample covariance matrix of the target dataset, and \bold{\bar{X}} is the mean vectors of the target dataset binded in n rows. When the population multivariate skewness is normal, the \frac{n}{6}b_{1,d} is asymptotically distributed as χ^2 distribution with d(d + 1)(d + 2)/6 degrees of freedom.

### Value

A value of a Mardia's multivariate skewness with a test statistic

### Author(s)

Sunthud Pornprasertmanit (psunthud@gmail.com)

### References

Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. doi:10.2307/2334770

### See Also

- `skew` Find the univariate skewness of a variable

- `kurtosis` Find the univariate excessive kurtosis of a variable

- `mardiaKurtosis` Find the Mardia's multivariate kurtosis of a set of variables

### Examples

    library(lavaan)
    mardiaSkew(HolzingerSwineford1939[ , paste0("x", 1:9)])

[Package semTools version 0.5-0 Index]